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TRS Standard pair #516965015
details
property
value
status
complete
benchmark
004.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.20370101929 seconds
cpu usage
5.900773284
max memory
4.7919104E8
stage attributes
key
value
output-size
8604
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 30 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) ATransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) app(app(sumwith, f), nil) -> nil app(app(sumwith, f), app(app(cons, x), xs)) -> app(app(plus, app(f, x)), app(app(sumwith, f), xs)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) app(app(sumwith, f), nil) -> nil app(app(sumwith, f), app(app(cons, x), xs)) -> app(app(plus, app(f, x)), app(app(sumwith, f), xs)) The set Q consists of the following terms: app(app(plus, 0), x0) app(app(plus, app(s, x0)), x1) app(app(sumwith, x0), nil) app(app(sumwith, x0), app(app(cons, x1), x2)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(plus, app(s, x)), y) -> APP(s, app(app(plus, x), y)) APP(app(plus, app(s, x)), y) -> APP(app(plus, x), y) APP(app(plus, app(s, x)), y) -> APP(plus, x) APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(plus, app(f, x)), app(app(sumwith, f), xs)) APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(plus, app(f, x)) APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(f, x) APP(app(sumwith, f), app(app(cons, x), xs)) -> APP(app(sumwith, f), xs) The TRS R consists of the following rules: app(app(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) app(app(sumwith, f), nil) -> nil app(app(sumwith, f), app(app(cons, x), xs)) -> app(app(plus, app(f, x)), app(app(sumwith, f), xs))
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